Improving reliability and reducing risk by using inequalities

The paper introduces a powerful domain-independent method for improving reliability and reducing risk based on algebraic inequalities, which transcends mechanical engineering and can be applied in many unrelated domains. The paper demonstrates the application of inequalities to reduce the risk of failure by producing tight uncertainty bounds for properties and risk-critical parameters. Numerous applications of the upper-bound-variance inequality have been demonstrated in bounding uncertainty from multiple sources, among which is the estimation of uncertainty in setting positioning distance and increasing the robustness of electronic devices. The rearrangement inequality has been used to maximise the reliability of components purchased from suppliers. With the help of the rearrangement inequality, a highly counter-intuitive result has been obtained. If no information about the component reliability characterising the individual suppliers is available, purchasing components from a single supplier or from the smallest possible number of suppliers maximises the probability of a high-reliability assembly. The Cauchy-Schwartz inequality has been applied for determining sharp bounds of mechanical properties and the Chebyshev's inequality for determining a lower bound for the reliability of an assembly. The inequality of the inversely correlated random events has been introduced and applied for ranking risky prospects involving units with unknown probabilities of survival

The asymptotic behaviour of a distributive sorting method

In the distributive sorting method of Dobosiewicz, both the interval between the minimum and the median of the numbers to be sorted and the interval between the median and the maximum are partitioned inton/2 subintervals of equal length; the procedure is then applied recursively on each subinterval containing more than three numbers. We refine and extend previous analyses of this method, e.g., by establishing its asymptotic linear behaviour under various probabilistic assumptions.sorting;probabilistic analysis

A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects

We propose a new transaction-level bivariate log-price model, which yields fractional or standard cointegration. The model provides a link between market microstructure and lower-frequency observations. The two ingredients of our model are a Long Memory Stochastic Duration process for the waiting times between trades, and a pair of stationary noise processes which determine the jump sizes in the pure-jump log-price process. Our model includes feedback between the disturbances of the two log-price series at the transaction level, which induces standard or fractional cointegration for any fixed sampling interval. We prove that the cointegrating parameter can be consistently estimated by the ordinary least-squares estimator, and obtain a lower bound on the rate of convergence. We propose transaction-level method-of-moments estimators of the other parameters in our model and discuss the consistency of these estimators. We then use simulations to argue that suitably-modified versions of our model are able to capture a variety of additional properties and stylized facts, including leverage, and portfolio return autocorrelation due to nonsynchronous trading. The ability of the model to capture these effects stems in most cases from the fact that the model treats the (stochastic) intertrade durations in a fully endogenous way.Tick Time; Long Memory Stochastic Duration; Information Share

On large deviations in queuing systems

The main purpose of the article is to provide a simpler and more elementary alternative derivation of the large deviation principle for compound Poisson processes defined

A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects

We propose a new transaction-level bivariate log-price model, which yields fractional or standard cointegration. To the best of our knowledge, all existing models for cointegration require the choice of a fixed sampling frequency Delta t. By contrast, our proposed model is constructed at the transaction level, thus determining the properties of returns at all sampling frequencies. The two ingredients of our model are a Long Memory Stochastic Duration process for the waiting times tau(k) between trades, and a pair of stationary noise processes ( e(k) and eta(k) ) which determine the jump sizes in the pure-jump log-price process. The e(k), assumed to be iid Gaussian, produce a Martingale component in log prices. We assume that the microstructure noise eta(k) obeys a certain model with memory parameter d(eta) in (-1/2,0) (fractional cointegration case) or d(eta) = -1 (standard cointegration case). Our log-price model includes feedback between the shocks of the two series. This feedback yields cointegration, in that there exists a linear combination of the two components that reduces the memory parameter from 1 to 1+d(eta) in (0.5,1) and (0). Returns at sampling frequency Delta t are asymptotically uncorrelated at any fixed lag as Delta t increases. We prove that the cointegrating parameter can be consistently estimated by the ordinary least-squares estimator, and obtain a lower bound on the rate of convergence. We propose transaction-level method-of-moments estimators of several of the other parameters in our model. We present a data analysis, which provides evidence of fractional cointegration. We then consider special cases and generalizations of our model, mostly in simulation studies, to argue that the suitably-modified model is able to capture a variety of additional properties and stylized facts, including leverage, portfolio return autocorrelation due to nonsynchronous trading, Granger causality, and volatility feedback. The ability of the model to capture these effects stems in most cases from the fact that the model treats the (stochastic) intertrade durations in a fully endogenous way.Tick Time; Long Memory Stochastic Duration; Information Share; Granger causality

The Theory from Large Deviations for Random Processes and Strong Convergence of Stochastic Approximation Procedures

This paper deals with the application of "large deviation" theory to the analysis of stochastic approximation procedures. The approach allows to get new results in the asymptotical behaviour of stochastic procedures under very mild assumption about the "noise". The paper contains a short but illuminative survey of these results together with some new author's findings. For applications the last section seems to be interesting presenting some new ideas in multiobjective optimization